Interpreting 3D axes | Year 8

01 / LEARN

Understand the idea.

Read the labels before the perspective

A flat drawing represents three perpendicular directions using a slanted view. Their apparent angles and drawn lengths can be misleading. Use the axis labels and numbered scale to identify $x$ , $y$ and $z$ rather than measuring the picture with a ruler.

Trace the diagram's dashed construction in coordinate order. It reaches $x = 2$ , then follows the $y$ direction to $y = 3$ , then follows the $z$ direction to $z = 2$ . These labelled values locate $Q (2, 3, 2)$ .

Labelled x, y and z axes have numbered one-unit steps. A dashed gold route reaches Q by following the x direction, then the y direction, then the z direction. The perspective projection does not preserve spatial lengths.

Use projection and checking

A movement parallel to one axis changes only that coordinate. Moving parallel to $z$ preserves $x$ and $y$ . Projecting a point vertically onto the $x y$ -plane therefore replaces its height with zero while keeping its floor position.

Check a plotted point by tracing its construction back through the labelled directions. Exact coordinates require a stated scale, tick values or dimension labels. If these are absent, the drawing's appearance alone does not justify inventing numerical coordinates.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read a construction

Use the labelled construction to state Q’s coordinates.

Worked solution

1
Read the first construction leg.
$x = 2$
The first leg follows the x-direction to the labelled value 2.
2
Read the depth leg.
$y = 3$
The next leg is parallel to the y-axis and reaches the labelled depth 3.
3
Read the height and assemble the triple.
$z = 2, Q = (2, 3, 2)$
The last leg reaches height 2; coordinates are reported in x,y,z order.

Answer

Q=(2,3,2).

EXAMPLE 02

Move parallel to an axis

A point starts at (2,3,2). It moves parallel to the z-axis until its height is 5. Find its new position.

Worked solution

1
Identify which coordinates stay fixed.
$x = 2, y = 3$
A move parallel to the z-axis changes neither across position nor depth.
2
Replace the height with the stated final value.
$z_{new} = 5$
The question gives the final height, so it replaces 2 rather than being added to it.
3
Write the new position.
$(2, 3, 5)$
Only the third coordinate changes during this vertical movement.

Answer

(2,3,5).

03 / YOUR TURN

Try it yourself.

Check your understanding

Drop (3,4,2) vertically to the xy-plane. What point is reached?

Show answer & reasoning

(3,4,0)

A vertical drop changes only $z$ . The $x y$ -plane has $z = 0$ , so $(3, 4, 2)$ projects to $(3, 4, 0)$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

State $Q$ ’s coordinates from the labelled diagram.
2 marks
From $(1, 2, 3)$ , move parallel to $x$ until $x = 4$ . State the new position.
2 marks
Find the floor projection of $(5, 1, 4)$ .
2 marks
A point is on the $y$ -axis with $y = 4$ . Write its coordinates.
2 marks
Can you read an exact point from an unlabelled 3D sketch with no scale? Explain.
2 marks
A construction reaches $(3, 0, 0)$ , then $(3, 2, 0)$ , then $(3, 2, 4)$ . Name the direction of each leg.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

State $Q$ ’s coordinates from the labelled diagram.
2 marks
Read the $x$ , then $y$ , then $z$ legs.
$(2, 3, 2)$
From $(1, 2, 3)$ , move parallel to $x$ until $x = 4$ . State the new position.
2 marks
Only the first entry changes.
$(4, 2, 3)$
Find the floor projection of $(5, 1, 4)$ .
2 marks
Set $z$ to zero, retaining $x$ and $y$ .
$(5, 1, 0)$
A point is on the $y$ -axis with $y = 4$ . Write its coordinates.
2 marks
On the $y$ -axis, $x$ and $z$ are zero.
$(0, 4, 0)$
Can you read an exact point from an unlabelled 3D sketch with no scale? Explain.
2 marks
A drawn length alone does not identify a coordinate value.
No. Axis identities and coordinate scales are missing.
A construction reaches $(3, 0, 0)$ , then $(3, 2, 0)$ , then $(3, 2, 4)$ . Name the direction of each leg.
2 marks
Each leg changes one coordinate from the previous point.
Positive $x$ , then positive $y$ , then positive $z$ .

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Coordinate transformations review; identifying positions using three coordinates; interpreting 3D axes; describing routes and relative positions; comparing diagrams, views and digital representations. This is spatial location, not senior vector algebra.

Official curriculum source ↗

In this lesson

Understand the idea.

Read the labels before the perspective

Use projection and checking

See the method in action.

Read a construction

Read the first construction leg.

Read the depth leg.

Read the height and assemble the triple.

Move parallel to an axis

Identify which coordinates stay fixed.

Replace the height with the stated final value.

Write the new position.

Try it yourself.

Check your understanding

Keep practising